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The position vector of the point of intersection of three planes r. \( \mathbf{n}_{1}=q_{1} \), r. \( \mathbf{n}_{2}=q_{2} \), r. \( \mathbf{n}_{3}=q_{3} \), where \( \mathbf{n}_{1}, \mathbf{n}_{2} \) and \( n_{3} \) are non-coplanar vectors, is
(a) \( \frac{1}{\left[\mathbf{n}_{1} \mathbf{n}_{2} \mathbf{n}_{3}\right]}\left[q_{3}\left(\mathbf{n}_{1} \times \mathbf{n}_{2}\right)+q_{1}\left(\mathbf{n}_{2} \times \mathbf{n}_{3}\right)+q_{2}\left(\mathbf{n}_{3} \times \mathbf{n}_{1}\right)\right] \)
(b) \( \frac{1}{\left[n_{1} n_{2} n_{3}\right]}\left[q_{1}\left(n_{1} \times n_{2}\right)+q_{2}\left(n_{2} \times n_{3}\right)+q_{3}\left(n_{3} \times n_{1}\right)\right] \)
(c) \( -\frac{1}{\left[n_{3} \mathbf{n}_{1} \mathbf{n}_{2}\right]}\left[q_{1}\left(\mathbf{n}_{1} \times \mathbf{n}_{2}\right)+q_{2}\left(\mathbf{n}_{2} \times \mathbf{n}_{3}\right)+q_{3}\left(\mathbf{n}_{3} \times \mathbf{n}_{1}\right)\right] \)
(d) None of the above
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